What was already known
Earlier results covered the planar case and coordinatewise unconditional bodies. The manuscript also notes Stancu’s all-dimensional announcement, with key flow-asymptotic details deferred; this provides a complete formalized argument for the selected statement.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Resolves the all-dimensional logarithmic Brunn–Minkowski conjecture for origin-symmetric convex bodies.
Limitations
The selected claim concerns Lebesgue volume of origin-symmetric bodies. The paper’s Lp, log-concave-measure, and B-conjecture consequences are outside the pinned Lean scope.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note gives the sharp logarithmic Wulff-volume inequality for all origin-symmetric convex bodies in every dimension.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For all origin-symmetric convex bodies K and L in every dimension and every interpolation parameter t in [0,1], the volume of their logarithmic Wulff combination is at least |K|^(1−t)|L|^t.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision